Not sure if anyone else experienced this issue; however, after updating to the Catalyst Beta 15.9 and 15.10, I was unable to launch Skyrim.
After selecting Play from the launcher window, for about 30 seconds, nothing would happen, then a windowed blackscreen would appear for an instant, followed by the "Failed to Initialize Renderer: Unknown Error Creating the Renderer" error message.
Tried several steps to fix this including updating SKSE, switching to the Steam downloaded version of SKSE, rebuilding the SkyrimPrefs.ini and Skyrim.ini, removing all mods, uninstalling Skyrim and downloading again from Steam, updating from Catalyst 15.9 Beta to 15.10 Beta, etc.
However, the only way I was able to resolve the issue was by rolling back to previous 15.7 (non-Beta) driver. Once I did this, the game launched normally. It seems the latest AMD Beta drivers are not compatible with Skyrim perhaps for certain older hardware.
(In case it's helpful, I'm using windows 7 64-bit with AMD 5830 Mobility graphics.)